SET007 Axioms: SET007+599.ax
%------------------------------------------------------------------------------
% File : SET007+599 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Propositional Calculus for Boolean Valued Functions. Part IV
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : bvfunc_8 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 29 ( 0 unt; 0 def)
% Number of atoms : 125 ( 26 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 125 ( 29 ~; 0 |; 0 &)
% ( 0 <=>; 96 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 8 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 0 prp; 1-4 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-3 aty)
% Number of variables : 96 ( 96 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k6_valuat_1(A,k6_valuat_1(A,C,D),E)) = k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,E)) ) ) ) ) ) ).
fof(t2_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k8_bvfunc_1(A,k8_bvfunc_1(A,C,D),E)) = k8_bvfunc_1(A,k8_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,D)),k14_bvfunc_1(A,B,E)) ) ) ) ) ) ).
fof(t3_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),E) = k8_bvfunc_1(A,k8_bvfunc_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,E)),k14_bvfunc_1(A,D,E)) ) ) ) ) ) ).
fof(t4_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),E) = k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,E),k14_bvfunc_1(A,C,E)),k14_bvfunc_1(A,D,E)) ) ) ) ) ) ).
fof(t5_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)) = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,D,B)),k14_bvfunc_1(A,C,B)),k14_bvfunc_1(A,B,D)) ) ) ) ) ).
fof(t6_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> B = k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,k5_valuat_1(A,C))) ) ) ) ).
fof(t7_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> B = k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,B,k5_valuat_1(A,C))) ) ) ) ).
fof(t8_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> B = k8_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),k6_valuat_1(A,k6_valuat_1(A,B,C),k5_valuat_1(A,D))),k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),D)),k6_valuat_1(A,k6_valuat_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) ).
fof(t9_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> B = k6_valuat_1(A,k6_valuat_1(A,k6_valuat_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),k5_valuat_1(A,D))),k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),D)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,D))) ) ) ) ) ).
fof(t10_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k6_valuat_1(A,B,C) = k6_valuat_1(A,B,k8_bvfunc_1(A,k5_valuat_1(A,B),C)) ) ) ) ).
fof(t11_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k8_bvfunc_1(A,B,C) = k8_bvfunc_1(A,B,k6_valuat_1(A,k5_valuat_1(A,B),C)) ) ) ) ).
fof(t12_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,C) = k5_valuat_1(A,k15_bvfunc_1(A,B,C)) ) ) ) ).
fof(t13_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,C) = k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) ) ) ) ).
fof(t14_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k19_bvfunc_1(A)) = k5_valuat_1(A,B) ) ) ).
fof(t15_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,k18_bvfunc_1(A)) = B ) ) ).
fof(t16_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k9_bvfunc_1(A,B,C) = k9_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) ).
fof(t17_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k5_valuat_1(A,k9_bvfunc_1(A,B,C)) = k9_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t18_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,C) = k6_valuat_1(A,k8_bvfunc_1(A,B,k5_valuat_1(A,C)),k8_bvfunc_1(A,k5_valuat_1(A,B),C)) ) ) ) ).
fof(t19_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,C) = k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) ) ) ) ).
fof(t20_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k19_bvfunc_1(A)) = B ) ) ).
fof(t21_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k15_bvfunc_1(A,B,k18_bvfunc_1(A)) = k5_valuat_1(A,B) ) ) ).
fof(t22_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k5_valuat_1(A,k15_bvfunc_1(A,B,C)) = k15_bvfunc_1(A,B,k5_valuat_1(A,C)) ) ) ) ).
fof(t23_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,k5_valuat_1(A,B),k15_bvfunc_1(A,k14_bvfunc_1(A,B,C),k5_valuat_1(A,B))) ) ) ) ).
fof(t24_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,k5_valuat_1(A,B),k15_bvfunc_1(A,k14_bvfunc_1(A,C,B),k5_valuat_1(A,C))) ) ) ) ).
fof(t25_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> r1_bvfunc_1(A,B,k15_bvfunc_1(A,k15_bvfunc_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,C,B)),B)) ) ) ) ).
fof(t26_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,B,k15_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,B))) = k19_bvfunc_1(A) ) ) ).
fof(t27_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),B),B) = k19_bvfunc_1(A) ) ) ) ).
fof(t28_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [E] :
( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,E)),k8_bvfunc_1(A,k5_valuat_1(A,D),k5_valuat_1(A,E))),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) = k19_bvfunc_1(A) ) ) ) ) ) ).
fof(t29_bvfunc_8,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [C] :
( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> ! [D] :
( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
=> k14_bvfunc_1(A,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) ).
%------------------------------------------------------------------------------